Tuesday, May 13, 2014

GTO Brainteaser #5 Solution: Bayesian Werewolves

This weeks solution is in video form:

The one aspect of the solution that is not covered in the video is the EV of the trial for an individual judge.

When all judges are playing the symmetric equilibrium strategy, the EV for a single judge is -102 when the accused is a human and 922 when the accused is a werewolf. If on average the accused is a werewolf 50% of the time then the EV of the trial is 410.

For comparison, if there were a single judge deciding honestly based solely on his own ritual result he would average 880 when the accused is a werewolf and -20 when then the accused is a human for an average EV of 430.

Even when all the judges have identical incentives, unanimity rule reduces their expectation.